Question: Rodney uses the following clues to try to guess a secret number:
\begin{tabular}{ c }
It is a two-digit integer.\\
The tens digit is odd.\\
The units digit is even.\\
The number is greater than 65.
\end{tabular}If Rodney guesses a number that has each of these properties, what is the probability that Rodney will guess the correct number? Express your answer as a common fraction.
Explanation: We need to count the number of two-digit integers with odd tens digit and even units digit that are greater than $65.$ Notice that the only two possibilities for the tens digit are $7$ and $9.$ For each of these, the units digits $0,$ $2,$ $4,$ $6,$ and $8$ are all possible, for a total of $5$ choices. Therefore there are $2\cdot 5=10$ possible integers to choose from. Since there are $10$ integers to choose from, the probability of selecting the right one is $\boxed{\frac{1}{10}}.$

For your information, the possible numbers are $$\{ 70, 72, 74, 76, 78, 90, 92, 94, 96, 98 \}.$$